Does the following inequality holds for every POSITIVE 'x' ?

  • #1
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does the following inequality holds for every POSITIVE 'x' ?

[tex] e^{-x}-1\le Cx^{1/4+e} [/tex] here 'C' and e are positive constants

i think that for very very small 'e' the constant must be very BIG but no other hint i find
 

Answers and Replies

  • #2
disregardthat
Science Advisor
1,854
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Certainly not without additional restrictions on e and C. (You should not use 'e' as a variable name to avoid confusion with e = 2.71...)

However, if e >= 1, the left hand side is non-positive, so in that case the equation words.
 

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